In reply to my own question, my findings:
Results Pageviews/Search
ga:pageviews[filter ga:pagePath=="/search"] / ga:uniquePageviews
[filter ga:pagePath=="/search"]
note that
ga:pageviews[filter ga:searchUsed=="Visits With Site Search"] /
ga:uniquePageviews[filter ga:searchUsed=="Visits With Site Search"]
gives a slightly bigger number than what is presented in GA portal
% Search Exits:
= ga:searchExits / ga:searchUniques
% Search Refinements
= ga:searchRefinements / ga:pageviews[filter ga:pagePath=="/search"]
note that we would have thought it would be
= ga:searchRefinements / ga:searchUniques
but that does not match what's on the GA portal
Time after Search
= ga:searchDepth / ga:searchUniques
Search Depth
= ga:searchDepth / ga:searchUniques
avg searches / Search visit
= ga:searchUniques / ga:searchVisits
onsite search visit rate
= ga:searchVisits / ga:visits